Leveraging the Value of Information in POMDP Planning

Beliefs in a Partially Observable Markov Decision Process (POMDP) are posterior distributions over the hidden state given the agent's history of actions and observations. They summarize everything the history says about the state, so planning in a POMDP is planning in a Markov decision process (MDP) over beliefs. Belief MDPs have continuous state spaces even for finite POMDPs, and exact planning in them is intractable in general. Planners must therefore approximate beliefs and estimate values. Monte Carlo planners do both inside a search tree, with an approximate belief at every node and a value estimate at every leaf. Approximations usually consist of sets of sampled states, with leaf values coming from rollouts, hand-designed bounds, or learned networks. Policies and values computed from these approximations are limited by their quality, and prior methods with learned networks rely on hand-chosen summaries of the sampled states. A belief representation should be computable from the parent node's representation through the POMDP's dynamics, let the search sample from it, and be learned so that it provides the information that policies and value functions need. We present Belief Embedding Tree Search (BETS), a Monte Carlo planner that meets these requirements by representing each node's belief with a generative distribution embedding (GDE) while updating it through the POMDP dynamics. BETS trains its belief model alongside its policy and value networks through experience, with the realized hidden state of the POMDP as the belief model's training target. We evaluate BETS on six configurations of RockSample, LightDark, and PocMan against BetaZero and three planners without learned components. BETS is competitive or leading on all six, while every baseline falls far behind on at least one. Where beliefs are highest-dimensional, it outperforms them by a large margin, even without search.

This paper presents a finite-time analysis for Monte Carlo Tree Search (MCTS) in Partially Observable Markov Decision Processes (POMDPs), with probabilistic concentration bounds in both discrete and continuous observation spaces. While MCTS-style solvers such as POMCP achieve empirical success in many applications, rigorous finite-time guarantees remain an open problem due to the nonstationarity and the interdependencies induced by heuristic action selection (e.g., UCB). In the discrete setting, we address these challenges by extending the polynomial exploration bonus to UCB in POMDP setting, yielding polynomial concentration bounds for the empirical value estimation at the root node. For continuous observation spaces, we introduce an abstract partitioning framework and propose a finite-time bound on partitioning loss. Under mild conditions, we prove highprobability bound on value estimates in POMDPs with continuous observation space. Specifically, we propose Voro-POMCPOW, a variant of POMCPOW with f inite-time guarantees that adaptively partitions the continuous observation space using Voronoi cells. This approach maintains a finite branching factor while preserving the original observation generator. Empirical validation demonstrates that the proposed Voro-POMCPOW shows competitive performance while providing theoretical guarantees. Although our analysis focuses on continuous POMDPs, the techniques developed herein are also applicable to continuous MDPs, closing another gap on the MDP side.

Planning under uncertainty is an essential capability for autonomous robots. The Partially Observable Markov Decision Process (POMDP) provides a powerful framework for such a capability. Although POMDP-based planning has advanced significantly, its application to real-world problems is often limited by the difficulty of obtaining faithful POMDP models. We present Vectorized Online planning wIth Learned diffusion model for POMDP Agents (VOiLA), a framework that learns task-agnostic POMDP models for online planning under uncertainty. VOiLA learns transition and observation samplers using conditional diffusion models and learns observation-likelihood models for particle-based belief updates. To enable efficient online planning, the diffusion samplers are distilled into compact feedforward generators and integrated with Vectorized Online POMDP Planner (VOPP), an online POMDP planner designed to leverage GPU parallelization. Experimental results indicate the distillation strategy reduces sampling cost by up to nearly three orders of magnitude, making learned generative POMDP models practical for online planning. Evaluation of VOiLA on three benchmark problems indicate that VOiLA achieves equal or better performance than Recurrent Soft Actor Critic while using less than 10% training data, and generalizes much better to unseen environment configurations. Physical robot evaluation indicates VOiLA uses the models learned using only simulated data and generates a policy that successfully accomplish the task in 10 of 10 runs.